Most released vapor is likely expelled out the chimney, plus due to increased humidity capacity of hot air it likely absorbs some from the home (especially with a fireplace, likely cooling down by absorbing water much faster than conducting its heat away) in some way before being expelled. A setup like this also likely causes a negative pressure, drawing air from outside which is also likely dry if it's winter cold.
Also, water vapor released through the chimney is lost energy (even if the steam isn't hot, moist air has more thermal capacity than dry air because water).